Block coordinate gradient (${\nabla }_{\mathcal{B}}f(x)={\sum }_{i\in \mathcal{B}}{\partial }_{i}f(x)e_i$)

The orthogonal projection of the gradient onto the coordinate subspace indexed by $\mathcal{B}$. It is kept as a vector in the original Euclidean space, with zero coordinates outside the block. For a singleton block it is ${\partial }_{i}f(x)e_i$; for the full block it is $\nabla f(x)$.

Target: gradient-descent.bigb, under Lipschitz gradient.